Each of the ten volumes of the collected works of Theodore Sturgeon is available in paperback for $\$$15 or in hardcover for $\$$25. Theresa buys a copy of each of the ten volumes for a total of $\$$220. How many hardcover volumes did she buy?
Say she bought $h$ hardcovers and $p$ paperbacks. She bought ten volumes total, so $h+p=10$. Her total cost, $25h+15p$, was $220$, or dividing by 5 $5h+3p=44$. Multiplying the first equation by 3 and subtracting it from the second, we get $5h-3h+3p-3p=2h=44-30=14$, or $h=\boxed{7}$.